Image Analysis by Scale-Space Operators

by Peter Johansen and Mads Nielsen

Over the last 5
years one of the key interests of the image analysis group at DIKU, Department
of Computer Science, University of Copenhagen has been the analysis of
images using scale-space operators. The aim has been to understand the
multi-scale structure of images and thereby facilitate automatic or semi-automatic
analysis of images. Tasks of interest are feature detection and segmentation
and computation of stereo disparity and optic flow.

At DIKU a group of approximately 5 researchers, lead by Prof. Peter
Johansen is involved in this project. The primary collaborative partner
is the 3D-Lab at the Medical Faculty, University of Copenhagen; where Mads
Nielsen is coordinating the application of scale-space techniques to medical
image analysis.

An image is digitally represented as intensity values on a pixel grid
spaced at some resolution. By convolving this image with Gaussians of increasing
width, a stack of images of gradually lower resolution than the original
image is constructed. This is the scale-space. In this way image details
are unconfounded from the pixel grid details, and the images at lower resolutions
(higher scales) are differentiable making the toolbox of differential geometry
available.

Convolving the image with Gaussians of increasing width causes the image
to gradually simplify. For example, regions merge into large regions (splits,
although rare, are also possible). In feature detection and image segmentation
this simplification can be exploited by initially analysing at a resolution
where the image is simple, and tracking the solution to a resolution where
localisation is more precise and shapes more complex. This idea has been
exploited in multi-scale image segmentation and in coarse-to-fine feature
detection.

The local derivatives of the image at a given scale have been used for
computation of the depth from a pair of stereo images, and also for computation
of the local surface orientation and shape. This work is based upon analysis
of how a deformation of the original image expresses itself in lower resolution
images. This analysis also leads to a reformulation of earlier optic flow
work in terms of scale-space.

From a CT-scan the bone structure is easily identified from iso-intensity
surfaces. Here also the muscular structure around the Jaw is identified
using a multi-scale, watershed based, semi-automatic, 3D segmentation technique.

The future direction of the project is to gain insight into the structural
changes of images as scale varies and exploit this especially in the field
of medical image analysis. This work is carried out in collaboration with
3D-Lab, Imaging Center Utrecht, Utrecht University Hospital, Royal Institute
of Technology, Stockholm, and Department of Vision Sciences, University
of Aston, Birmingham.